It is possibly to prevent her death; don't progress in the main storyline far enough to cause her to die. This will prevent you from completing the main story, but you will have saved her life! Is finishing the game really worth Aeris' life?

No, but you can see her again. On disc three, revisit the church in Midgar in the Sector 5 slums. A silhouette of Aeris (or her "ghost" as some fans will say) will appear near the flower patch for a brief moment.

Aside from that, only cheats (gameshark, etc.) can get her back to your party.

There was a rumor I read that there was going to be a way to resurect Aris, but due to time restraints for the Japan launch this was taken out. And aparently there are a few dead end dialogues and mini side quests around that don't lead to anything but where for the purpose of this.

The USA version has an extra FMV and other bits added in that they didn't have time for in the Jap version, however it's all minor and If the rumor of time was the reason she couldn't be brought back to life then this is a good thing as it add's a great level of emotion to the game.

@spartacus The FF series itself is what died in FF8.
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FambidaJul 6 '13 at 18:23

@Fambida: Meh. All FF8 did was take all of the things FF7 got wrong and double down on them. Neither game has got a thing on the SNES Final Fantasy titles, either story-wise or gameplay-wise.
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Mason WheelerJun 30 at 21:14